Although reliable mobile wireless transmission of video, data, and speech at high rates to many users will be an important part of future telecommunications systems, there is considerable uncertainty as to what technologies will achieve this goal. One way to get high rates on a scattering-rich wireless channel is to use multiple transmit and/or receive antennas. Many of the practical schemes that achieve these high rates require the propagation environment or channel to be known to the receiver.
In practice, knowledge of the channel is often obtained via training: known signals are periodically transmitted for the receiver to learn the channel, and the channel parameters are tracked (using decision feedback or automatic-gain-control (AGC)) in between the transmission of the training signals. However, it is not always feasible or advantageous to use training-based schemes, especially when many antennas are used or either end of the link is moving so fast that the channel is changing very rapidly.
Hence, there is much interest in space-time transmission schemes that do not require either the transmitter or receiver to know the channel. A standard method used to combat fading in single-antenna wireless channels is differential phase-shift keying (DPSK). In DPSK, the transmitted signals are unit-modulus (typically chosen from a m-PSK set), information is encoded differentially on the phase of the transmitted signal, and as long as the phase of the channel remains approximately constant over two consecutive channel uses, the receiver can decode the data without having to know the channel coefficient.
Differential techniques for multi-antenna communications have been proposed, where, as long as the channel is approximately constant in consecutive uses, the receiver can decode the data without having to know the channel. The general differential techniques of the Background Art have good performance when the set of matrices used for transmission forms a group under matrix multiplication, which also leads to simple decoding rules.
But the number of groups available is rather limited, and the groups do not lend themselves to very high rates (such as tens of bits/sec/Hz) with many antennas. One of the Background Art techniques is based on orthogonal designs, and therefore has simple encoding/decoding and works well when there are two transmit and one receive antenna, but suffers otherwise from performance penalties at very high rates.
Part of the difficulty of designing large sets of unitary matrices is the lack of simple parameterizations of these matrices. To keep the transmitter and receiver complexity low in multiple antenna systems, linear processing is often preferred, whereas unitary matrices are often highly nonlinear in their parameters.